A theoretical and computational study of the FRF-based substructuring technique applying enhanced least square and TSVD approaches

The frequency response function (FRF)-based substructuring technique has been previously proposed for computing the vibratory response of complex built-up structures with moderately high-modal density characteristic. This is because it has the advantage of being able to incorporate experimental component FRFs directly into its spectral formulation. However, the accuracy of this technique is frequently hindered by spectral distortion problem due to amplification of errors in the FRF-matrix during an inversion calculation. To analyze the influence of error amplification, its inherent FRF-matrix inverse problem is mathematically transformed into an over-determined set of linear algebraic equations. The least-squares (LS) and total least-squares (TLS) solution schemes are proposed to handle this new formulation. It is then shown that these two proposed algorithms can lead to some improvements in the predictions but cannot eliminate the influence of error completely. To further achieve more accurate dynamic coupling response, the truncated singular value decomposition (TSVD) scheme is proposed to work in conjunction with the LS and TLS algorithms. Its effectiveness in reducing the influence of pre-existing errors in the FRF-matrix when applying this type of substructuring technique to a two-component system is investigated theoretically and computationally. This study also led to the discovery of certain new condition under which the TSVD scheme is most effective.